Like Styrak said, the "400 fps w/ .2g" is a standard measure, its not just 400 fps with any BB weight (in which case chronying 400 fps using .30g BB, for example, would yield a much higher velocity when using .20g).

Usually events let you use whatever BB weight you want, although there are some exceptions, usually in indoor/CQB games where engagement distances are reduced (heavier BBs have more inertia and carry energy further, so at short ranges the energy in impact is closer to point blank shot, increasing the risk of injury).

Note that some organizers opt to use muzzle energy as a limit instead, so they'll chrony guns with whatever weight BB you're using on the field and calculate muzzle energy (or more precisely, they have a pre-calculated limit chart for all BB weights) -- the limit usually being ~1.5 joules which is roughly the energy of a 0.2g projectile at 400 fps.